Systems and methods for collapsible structure applications

ABSTRACT

Collapsible structures may be formed from planar solids. The structures may be comprised of multiple planar objects hingedly connected, where each planar object may include magnetic materials (e.g., magnets, ferromagnetic metals) or electromagnetic materials. Using the magnetic or electromagnetic materials, the connected planar objects may be arranged as a single planar object with multiple layers, or may be arranged as a three-dimensional (3-D) object, where the magnetic or electromagnetic materials may be used to retain the formed 3-D object shape. Application of a current to the electromagnetic materials may cause the collapsible structure to form the 3-D object, and removal of the electric current may cause the collapsible structure to revert to a single planar object. Multiple structures may be combined to form larger structures.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 14/245,249, filed Apr. 4, 2014, the content ofwhich is hereby incorporated in its entirety.

FIELD

The present invention relates to collapsible structures, andspecifically to magnetic educational collapsible structures.

BACKGROUND

Planar geometric structures may be assembled in various configurationsto form different three-dimensional (3-D) geometric structures, and maybe collapsed into substantially planar configurations. The structuresmay be used as an educational toy by children, or may be used by adultsor children to explore various two-dimensional or three-dimensionalshapes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front view of a planar shape that may be used to form acollapsible structure.

FIGS. 2A-2B are front and perspective views of three planar shapesjoined on different sides to form a 3-D geometric structure.

FIGS. 3A-3B are front and perspective views of three planar shapesjoined on a single side to form a 3-D geometric structure.

FIGS. 4A-4B are perspective views of combining two 3-D geometricstructures to form a larger 3-D geometric structure.

FIGS. 5A-5B are perspective views of combining four 3-D geometricstructures to form a dodecahedron.

FIG. 6 is a perspective view of a modified dodecahedron formed from fourcollapsible structures.

FIG. 7 is a perspective view of a tetrahedral building block.

FIG. 8 is a perspective view of two tetrahedral building blocks nestedtogether.

FIGS. 9A-9B are perspective views of combining four tetrahedral buildingblocks at separate corners.

FIG. 10 is a perspective view of multiple tetrahedral building blockscombined to form an extended tetrahedral structure.

FIG. 11 is a perspective view of a tetrahedrally supported six-sided 3-Dgeometric structure.

FIGS. 12A-12C are perspective views of combining four tetrahedralbuilding blocks to form a neutral converter.

FIGS. 13A-13B are perspective views of combining two neutral convertersto form a positive universal joint.

FIGS. 14A-14B are perspective views of combining six tetrahedralbuilding blocks to form a turbine connector.

FIGS. 15A-15B are perspective views of combining two neutral convertersto form a negative universal joint.

FIGS. 16A-16B are perspective views of combining eight tetrahedralbuilding blocks to form a phase capacitor coupling.

DETAILED DESCRIPTION

Collapsible structures may be formed from planar solids. The structuresmay be comprised of multiple planar objects hingedly connected, whereeach planar object may include magnetic materials (e.g., magnets,ferromagnetic metals) or electromagnetic materials. Using the magneticor electromagnetic materials, the connected planar objects may bearranged as a single planar object with multiple layers, or may bearranged as a three-dimensional (3-D) object, where the magnetic orelectromagnetic materials may be used to retain the formed 3-D objectshape. Application of a current to the electromagnetic materials maycause the collapsible structure to form the 3-D object, and removal ofthe electric current may cause the collapsible structure to revert to asingle planar object. Multiple structures may be combined to form largerstructures.

Collapsible structures may be formed from one or more basic polygons orother shapes. Collapsible structures may include magnetic materials(e.g., magnets, ferromagnetic metals), piezoelectric materials, orlights (e.g., LEDs). Collapsible structures may be combined to form orgive the appearance of various geometric structures, and the includedmagnetic materials may be used to retain the formed geometric structureshape. A collapsible structure may be formed from six pentagons, and maybe referred to as a “lynch pin” structure.

In the following description, reference is made to the accompanyingdrawings that form apart hereof and in which is shown by way ofillustration specific embodiments that may be practiced. Theseembodiments are described in sufficient detail to enable those skilledin the art to practice the invention, and it is to be understood thatother embodiments may be utilized and that structural, logical, andelectrical changes may be made without departing from the scope of thepresent invention. The following description of example embodiments is,therefore, not to be taken in a limited sense, and the scope of thepresent invention is defined by the appended claims.

FIG. 1 is a front view of a planar shape 100 that may be used to form acollapsible structure, according to an embodiment. The planar shape maybe a regular polygon, such as the regular pentagon 110. In someembodiments, the planar shape may be substantially two-dimensional. Inother embodiments, the planar shape edges include various features thatallow two or more planar shapes to connect to each other.

FIGS. 2A-2B are front and perspective views of three planar shapesjoined on different sides to form a 3-D geometric structure 200,according to an embodiment. The planar shapes may include three regularpentagons 210, 220, and 230. Two or more of the pentagons may beattached on a side to form a hinge, such as is shown in FIG. 2A. Eachhinge may be constructed using a flexible material or a mechanicalhinge. In some embodiments, one or more of the planar shapes may becollapsed (e.g., closed) toward each other, and may form a 3-D shape.For example, pentagons 220 and 230 shown in FIG. 2A may be folded towardeach other to form the 3-D shape shown in FIG. 2B. In other embodiments,one or more of the planar shapes may be collapsed (e.g., closed) towardeach other to become flush (e.g., coplanar) to form a multiple layer,substantially planar object. For example, pentagons 220 and 230 shown inFIG. 2A may be folded toward each other to form a single, three-layerpentagon.

FIGS. 3A-3B are front and perspective views of three planar shapesjoined on a single side to form a 3-D geometric structure 300, accordingto an embodiment. The planar shapes may include three regular pentagons310, 320, and 330. The planar shapes may be joined on a common edge toform a 3-D structure, such as is shown in FIGS. 3A-3B.

FIGS. 4A-4B are perspective views of combining two 3-D geometricstructures to form a larger 3-D geometric structure 400, according to anembodiment. Two 3-D geometric structures may be joined together to forma larger 3-D geometric structure. In an example, the 3-D geometricstructure 300 shown in FIG. 3B may be attached to the 3-D geometricstructure 200 shown in FIG. 2B. In this example, point 410 may be joinedto point 415, point 420 may be joined to point 425, point 430 may bejoined to point 435, and point 440 may be joined to point 445 to form asix-sided 3-D geometric structure 400 shown in FIG. 4B.

The six-sided 3-D geometric structure 400 shown in FIG. 4B may includefour pyramidal inner spaces 450, 455, 460, and 466. Each pyramidal innerspace may be shaped similar to the 3-D shape shown in FIG. 2B. Theplanar pentagonal surfaces may include magnetic materials orelectrically conductive lines, and may be used to create or modify amagnetic field or an electric field. The magnetic or electric field mayhave an associated resonance. The magnetic or electric field may becreated or modified for the entire six-sided 3-D geometric structure400, or the magnetic or electric field may be created or modifiedseparately modified for each of the four pyramidal inner spaces 450,455, 460, and 466.

Power may be provided to the electrically conductive planar shapesthrough a power storage element (e.g., capacitor, battery) or through apower-generating element (e.g., solar cell, piezoelectric component).For example, a piezoelectric component may be used to convert sound intoelectricity, and the electricity may be used to create an electric fieldaround one or more of the four pyramidal inner spaces 450, 455, 460, and466.

Various sides may be joined using hinges, and may be collapsed towardeach other to form a multiple layer, substantially planar object.Various sides may be held in a fixed position using magnetic orelectromagnetic materials. For example, a multiple layer, substantiallyplanar object may be manually arranged into the six-sided 3-D geometricstructure 400 shown in FIG. 4B. Various sides may be moved into aselected position using magnetic or electromagnetic materials. Forexample, applying a magnetic or electromagnetic field to a multiplelayer, substantially planar object may cause the object to be arrangedinto the six-sided 3-D geometric structure 400 shown in FIG. 4B.

FIGS. 5A-5B are perspective views of combining four 3-D geometricstructures to form a dodecahedron 500, according to an embodiment. Four3-D geometric structures may be joined together to form a larger 3-Dgeometric structure. For example, a dodecahedron may be formed bycombining twelve regular pentagons. Each of the 3-D geometric structuresshown in FIG. 2B includes three connected pentagons, as shown in variousorientations in FIG. 5A as 510, 520, 530, and 540. Four of thesestructures may be combined to form a twelve-sided dodecahedron as shownin FIG. 5B.

FIG. 6 is a perspective view of a modified dodecahedron 600 formed fromfour collapsible structures, according to an embodiment. A dodecahedronmay include one or more collapsible surfaces. Instead of forming adodecahedron as described and shown with respect to FIGS. 5A-5B, adodecahedron may be formed from four of the six-sided 3-D geometricstructures shown in FIG. 4B, as shown in various orientations in FIG. 6as 610, 620, 630, and 640, Various surfaces may be moved into a selectedposition using magnetic or electromagnetic materials. For example,applying a magnetic or electromagnetic field may cause the object to bearranged into the modified dodecahedron 600 shown in FIG. 6. Eachmodified dodecahedron 600 may be used as a building block, and theplanar surfaces extending beyond the twelve-sided dodecahedron surfacemay be used to combine two or more modified dodecahedrons 600.

FIG. 7 is a perspective view of a tetrahedral building block 700. Thetetrahedral building block 700 may include four connected circularfaces. The flanges of four such circular faces may be connected to formtetrahedral flanges 710, 712, 716, 718, and 720. The circular faces maybe connected such that the flanges 710, 712, 716, 718, and 720 are flat,and the triangles inscribed in each of the four connected circular facesmay form a tetrahedral inner space 730. In other embodiments, thecircular faces may be connected at or near the circumference of eachcircular face such that the flanges 710, 712, 716, 718, and 720 definean inner volume (e.g., inner pocket). The outermost arcuate portions ofthe tetrahedral flanges 710, 712, 716, 718, and 720 may define aspherical volume that corresponds with the circumscribed sphere (e.g.,circumsphere) surrounding the tetrahedral inner space 730.

The tetrahedral building block 700 may be transparent, may betranslucent, may include a semi-transparent material comprised of acolor, or may include a solid (e.g., opaque) material. The tetrahedralinner space 730 may include one or more gasses, such as noble gasses orgasses that are translucent or colored. The tetrahedral inner space 730may include one or more fluids (e.g., gasses or liquids). The fluid maybe selected according to its response to solar heating. For example, afluid may expand in response to solar heating and cause the flanges toopen. In another example, a fluid with a high heat capacity may storeenergy received from solar heating, such as in concentrated solar powerapplications. The fluid may be selected according to its ability tochange color or light absorption. For example, a suspended particlefluid may transition from a clouded appearance to a translucentappearance in the presence of an electrical voltage. Various levels oftransparency or various shades of color may be used for the each side ofthe tetrahedral inner space 730 or for each of the tetrahedral flanges710, 716, 718. The use of semi-transparent materials of various colorsmay allow the colors to be combined depending on orientation. Forexample, if the device is held so a blue face is superimposed on ayellow face, the object may appear green. Similarly, multipletetrahedral building blocks 700 may be combined to yield various colors.Multiple tetrahedral building blocks 700 may be combined to form theappearance of various platonic solids, where the platonic solidappearance may depend on each tetrahedral building block's specificperiodicities of motion and wave positions in time as indicated by thedirection of particular intersecting linear projections. For example,the vertices of four tetrahedral building blocks 700 using tetrahedralconfigurations may be combined to form a larger tetrahedron, where thelarger tetrahedron maintains the one hundred and twenty degree angle ateach of its vertices. Multiple tetrahedral building blocks 700 may becombined to form various other building blocks, such as is shown inFIGS. 12-16.

FIG. 8 is a perspective view 800 of two tetrahedral building blocksnested together. At least one tetrahedral surface may be collapsed orremoved, such as surface 810. Two or more tetrahedral building blocks700 may be nested, and may be connected at one or more connection pointsvia mechanical, magnetic, or by other means. For example, magneticflange 812 may adhere to magnetic tetrahedral inner space 822, flange814 may adhere to space 824, and flange 816 may adhere to space 826.Multiple tetrahedral building blocks 700 may be nested on one or more ofthe four tetrahedral vertices as shown in FIGS. 9A-9B.

FIGS. 9A-9B are perspective views of combining four tetrahedral buildingblocks at separate corners 900. FIG. 9A shows a simplified version offour tetrahedral shapes (e.g., pyramids) with collapsed sides 912, 914,916, and 918, and one base tetrahedral shape 920 with no collapsedsides. In an example, three of the four tetrahedral shapes 914, 916, 918are nested on the bottom three vertices of the base tetrahedral shape920 to form a tripod configuration, and one tetrahedral shape 912 may benested on the top vertex of the base tetrahedral shape 920. FIG. 9Bshows an analogous configuration using tetrahedral building blocks,including four tetrahedral building blocks with collapsed sides 932,934, 936, and 938, and one base tetrahedral building block 940 with nocollapsed sides. In an example, three of the four tetrahedral buildingblocks 934, 936, and 938 are nested on the three bottom three verticesof the base tetrahedral building block 940 to form a tripodconfiguration, and one tetrahedral building block 932 may be nested onthe top vertex of the base tetrahedral building block 940. Additionaltetrahedral building blocks with collapsed sides may be added on to eachof the four tetrahedral building blocks with collapsed sides 932, 934,936, and 938 to form larger structures, as shown in FIG. 10.

FIG. 10 is a perspective view of multiple tetrahedral building blockscombined to form an extended tetrahedral structure 1000. The extendedtetrahedral structure 1000 may include four branches of tetrahedralbuilding blocks with collapsed sides 1012, 1014, 1016, and 1018, and onebase tetrahedral building block 1020 with no collapsed sides. Theextended tetrahedral structure 1000 may form an interior of a structure,such as the six-sided 3-D geometric structure 400 shown in FIG. 4B.Additional nested tetrahedral building blocks may be used to form all ofthe edges and vertices of the six-sided 3-D geometric structure 400,such as is shown in FIG. 11.

FIG. 11 is a perspective view of a tetrahedrally supported six-sided 3-Dgeometric structure 1100. Each of the four branches of tetrahedralbuilding blocks shown in FIG. 10 may be extended to form a newfour-branch vertex, such as at four-branch vertex 1110. From each of thefour-branch vertices at the ends of the four branches, additionaltetrahedral building blocks may be used to extend additional branches toa two-branch vertex, such as at two-branch vertex 1120. This structuremay be used to form the edges for a structure, such as the six-sided 3-Dgeometric structure 400 shown in FIG. 4B. Each of the planar surfaceswithin the tetrahedrally supported six-sided 3-D geometric structure1100 may be pentangular, and may be supported by one or moresubstantially planar pentangular reinforcements or circularreinforcements, such as shown at circular inner surface 1130.

FIGS. 12A-12C are perspective views of combining four tetrahedralbuilding blocks to form a neutral converter 1200. The tetrahedralbuilding blocks 700 shown in FIG. 12A may be connected at a singlevertex to form a rigid or semirigid neutral converter 1200.Alternatively, the rigid or semirigid neutral converter 1200 may beformed by arranging the tetrahedral building blocks 700 no that theirvertices and flanges meet as shown in FIG. 12B, for example byconnecting various tetrahedral building block flanges to the triangularsurfaces of neighboring tetrahedral building blocks 700, such as isshown in FIG. 12B. The tetrahedral building blocks 700 may be connectedvia mechanical, magnetic, or by other means. For example, a magneticflange may adhere to a magnetic triangular surface or inner volume, suchas shown in FIG. 8.

A neutral converter 1200 top view is shown in FIG. 12B. One portion ofone or more of the tetrahedral building blocks may extend beyond thecentral portion of the neutral converter 1200, and may be used toconnect with various other structures. For example, the three exposedflanges 1210 may be used to fit within the hexagonal inner space of theturbine connector 1400 shown in FIG. 14B.

A neutral converter 1200 bottom view is shown in FIG. 12C. The innerspace formed at the connection of the tetrahedral building blocks 700may form a square pyramid inner space 1220. Flanges 1222, 1224, 1226, or1228 may extend beyond the four sides of the square pyramid inner space1220. A neutral converter 1200 may be connected using flanges 1222,1224, 1226, or 1228 to another neutral converter 1200 to form a positiveuniversal joint as shown in FIGS. 13A-13B.

FIGS. 13A-13B are perspective views of combining two neutral convertersto form a positive universal joint 1300. The square pyramid inner space1220 of two neutral converters 1200 may be mated, as shown in FIG. 13A.The flanges of these two neutral converters 1200 may be connected toform a rigid or semirigid positive universal joint 1300. Within thepositive universal joint 1300, the square pyramid inner space of eachneutral converter 1200 may combine to form an octahedral inner space1310. One portion of one or more of the tetrahedral building blocks 1320may project from the positive universal joint 1300, and may be used toconnect with various other structures. For example, the three exposedflanges 1322, 1324, and 1326 may be used to fit within the hexagonalinner space of the turbine connector 1400 shown in FIG. 14B.

FIGS. 14A-14B are perspective views of combining six tetrahedralbuilding blocks to form a turbine connector 1400. Six tetrahedralbuilding blocks 700 may be rotated and combined on two or more flangesto form a rigid or semirigid turbine connector 1400, as shown in FIG.14A. The tetrahedral building blocks 700 may be combined in a consistentorientation to form a hexagonal inner space 1410, as shown in FIG. 14B.The turbine connector 1400 may be placed on a positive universal joint1300, where the hexagonal inner space 1410 of the turbine connector 1400may mate with the three flanges 1322, 1324, and 1326 of a tetrahedralbuilding blocks 700 projecting from a positive universal joint 1300.

FIGS. 15A-15B are perspective views of combining two neutral convertersto form a negative universal joint 1500. The square pyramid inner space1220 of two neutral converters 1200 may be arranged in oppositedirections, as shown in FIG. 13A, and one or more of the adjacentflanges may be connected to form a rigid or semirigid negative universaljoint 1500. Within the negative universal joint 1500, the square pyramidinner space of each neutral converter 1200 may be arranged to be on theoutside of the negative universal joint 1500, such as the square pyramidinner space 1510 shown in FIG. 15B. A negative universal joint 1500 maybe combined with an additional neutral converter 1200, where the flangesof two square pyramid inner spaces may be connected, and the squarepyramid inner space of each neutral converter 1200 may combine to form arigid or semirigid hybrid positive-negative universal joint. One or moreof the constituent tetrahedral building blocks 700 may project from thehybrid positive-negative universal joint, and may be combined with theturbine connector shown in FIGS. 14A-14B.

FIGS. 16A-16B are perspective views of combining eight tetrahedralbuilding blocks to form a phase capacitor coupling 1600. The tetrahedralbuilding blocks 700 shown in FIG. 16A may be loosely connected at asingle vertex or flange to form a flexible phase capacitor coupling 1600shown in FIG. 16B. In contrast to the rigid or semirigid structure inthe neutral converter 1200, positive universal joint 1300, turbineconnector 1400, or negative universal joint 1500, the tetrahedralbuilding blocks 700 within the phase capacitor coupling 1600 can movefreely with respect to each other. The constituent tetrahedral buildingblocks 700 may be connected using various tetrahedral building blocksflanges, using a flexible wire, using magnetic elements, or using otherflexible connections. Eight tetrahedral building blocks 700 may beloosely connected to form a symmetrical phase capacitor coupling 1600,though a different number of tetrahedral building blocks 700 may beused.

In various embodiments, the collapsible structures or tetrahedralbuilding blocks may be transparent, may be translucent, may include asemi-transparent material comprised of a color, or may include a solid(e.g., opaque) material. One or more light emitting diodes (LEDs) may beembedded within a planar surface. For example, LEDs may be connected toelectrically conductive grid lines within the planar surfaces, and mayreceive power through the grid lines. Power may be provided to the LEDsthrough a power storage element (e.g., capacitor, battery) or through apower-generating element (e.g., solar cell, piezoelectric component).The electrically conductive grid lines may conduct power to the LEDs forlighting purposes. For example, the six-sided 3-D geometric structure400 shown in FIG. 4B or the modified dodecahedron 600 shown in FIG. 6may be used as a light fixture.

The electrically conductive grid lines may conduct power to the LEDs foreducational purposes. For example, two enhanced devices may detectproximity using a magnetic or other proximity detection mechanism, andthe proximity detection may convey power to the LEDs to indicate thatthe enhanced devices have been placed in the correct arrangement. Theelectrically conductive grid lines may serve as contour lines foreducational purposes. For example, a two-dimensional surface with a gridpattern may be used to form one or more curved planar surfaces, and thecurved planar surfaces will exhibit a visual distortion of the gridpattern according to the curvature of each surface. In another example,one or more planar surfaces may be formed using organic light emittingdiodes (OLEDs) or liquid crystal displays (LCDs), and may displayvarious human-readable or machine-readable information.

The collapsible structure may alter its appearance based on the presenceof electrical current, an electric or magnetic field, sound vibration,or other external force. The collapsible structure may include one ormore piezoelectric component, and this piezoelectric component mayconvert between mechanical and electrical inputs. A quartz piezoelectricelement may be included at each of the vertices in the collapsiblestructure, and may be used to generate power for one or more LEDs. Forexample, sound vibration may be received through a planar surface ordirectly at a piezoelectric element, and the piezoelectric element maycause one or more LEDs to alter color or intensity according to thepattern of received sound vibration.

The piezoelectric element may be used for educational purposes. Forexample, two enhanced devices may detect proximity using a magnetic orother proximity detection mechanism, and the proximity detection mayconvey power to the piezoelectric element to generate a sound toindicate that the enhanced devices have been placed in the correctarrangement. One or more mechanical or electromechanical resonantdevices may be used to modify, propagate, amplify, or mitigateexternally applied vibration. For example, a mechanical tuning fork maybe used to amplify vibration induced in a piezoelectric element.

In some embodiments, using electrochemical materials, application of anelectrical current may transition one or more surfaces of thecollapsible structure to translucent, clouded, or colored. A solidcollapsible structure may be used to conduct vibration, such as inacoustic or other applications. For example, induced mechanicalvibration may be used in vibration therapy. The collapsible structuremay be constructed using a conductive material for various electricalapplications. For example, one or more of the faces of the collapsiblestructure may be comprised of silicon, where the silicon is arranged tofunction as a resistor, inductor, capacitor, transistor, completemicrochip (e.g., integrated circuit), or other electrical component.Multiple collapsible structures or tetrahedral building blocks may bearranged to propagate conducted vibration. For example, a mechanicalvibration may be generated by applying an electric current to apiezoelectric element in a first structure, and this vibration may beconducted by the second structure and converted to an electricalimpulse.

The collapsible structure may be made of a transparent material, and maybe of a uniform or nonuniform thickness. The collapsible structure mayinclude one or more photovoltaic cells, and may be used in solar powerapplications. For example, the cross-section of the collapsiblestructure may be convex or concave, and may be used as a lens in variousoptical applications. The collapsible structure may include variouscolor patterns. Various additional ornamental designs may be used oneach side of the collapsible structure. Various designs may includelines comprised of magnetic tape, where information may be encoded ortransferred using the magnetic tape. For example, standard magnetic tapeencoders and readers may be used to record or read information encodedon a magnetic tape stripe on an exterior surface. Various designs mayinclude lines comprised of electrically conductive materials, such ascopper. The collapsible structure may be constructed using a flexiblematerial to allow the three faces to expand or contract.

The lines within each enhanced device may be uniformly distributed. Forexample, a circular enhanced template may include a series of arcsradiating from the circle center to the circle radius, where each arc isspaced apart from adjacent arcs by forty-five degrees. Enhanced devicescorresponding to this circular two-dimensional enhanced template mayhave corresponding arc portions, and the arc portions may aid the userin arranging the enhanced devices on the template. In other embodiments,the grid lines may be irregular in shape or spacing, may be configuredin a fractal pattern, or may be configured in another arrangement.

The inner space may include one or more gasses, such as noble gasses orgasses that are translucent or colored. The inner space may include oneor more fluids (e.g., gasses or liquids). The fluid may be selectedaccording to its response to heating or cooling. In another example, afluid with a high heat capacity may store energy received from solarheating, such as in concentrated solar power applications. The fluid maybe selected according to its ability to change color or lightabsorption. For example, a suspended particle fluid may transition froma clouded appearance to a translucent appearance in the presence of anelectrical voltage. Various levels of transparency or various shades ofcolor may be used. The use of semi-transparent materials of variouscolors may allow the colors to be combined depending on orientation. Forexample, if the device is held so a blue face is superimposed on ayellow face, the object may appear green. Similarly, multiplecollapsible structures or tetrahedral building blocks may be combined toyield various colors. Multiple collapsible structures or tetrahedralbuilding blocks may be combined to form the appearance of variousplatonic solids, where the platonic solid appearance may depend on eachcollapsible structure's specific periodicities of motion and wavepositions in time as indicated by the direction of particularintersecting linear projections. For example, the vertices of multiplecollapsible structures or tetrahedral building blocks may be combined toform a larger enhanced device.

The planar shapes may be collapsed or opened fully or partially throughvarious methods. The planar shapes may be collapsed or opened by variousactive mechanical or electromechanical devices. These devices mayinclude hydraulic actuators, servos, or other mechanical orelectromechanical means. For example, the planar shapes or innertetrahedral surfaces may contain magnetic or electromagnetic material,and one or more electromagnets may be energized selectively to collapseor open one or more planar shapes. An electromagnetic field may be usedto cause movement of one or more planar shapes, or may be used toarrange two or more enhanced devices in a predetermined configuration.In embodiments where the planar shapes define an inner volume, theplanar shapes may be collapsed or opened by heating or cooling a fluid(e.g., increasing or decreasing molecular vibration) contained withinthe enhanced device. For example, the fluid may be heated using solarenergy, and the expanding fluid may fill the planar shapes and causethem to open. The planar shapes may be collapsed or opened by variouspassive methods, such as collapsing and opening opposing planar shapesalternatingly in response to a fluid. For example, a moving fluid suchas wind may open a flange and cause the enhanced device to rotate aroundits axis of symmetry, and as the flange rotates into the wind, the windmay collapse that flange.

In some embodiments, the surfaces may also be collapsed or removed toallow nesting (e.g., stacking) of two or more collapsible structures ortetrahedral building blocks. Two or more collapsible structures ortetrahedral building blocks may be nested, and may be connected at oneor more connection points via mechanical, magnetic, or by other means.For example, a magnetic flange may adhere to magnetic inner volume.Multiple enhanced devices may be nested on one or more of the verticesof the contracted triangular faces. For example, multiple devices may benested on the three bottom vertices to form a tripod configuration, andmultiple devices may be nested on the top vertex to form a verticalcolumn. In an additional example, a second nested tripod configurationcould be arranged on the vertical column, where each of the three tripodlegs serves as a counterbalance for the other two tripod legs. Enhanceddevices may be designed asymmetrically so that a series of collapsiblestructures or tetrahedral building blocks may be connected to form acircle, polygon, or other shape. Any combination of nested enhanceddevices may be used to form larger structures. Nested enhancedstructures may be expanded or reinforced by adding additional shapes.

Additional embodiments using regular polygons may have a number of sidesthat are integer multiples of three, including the hexagon with sixtydegree interior angles, a twelve-sided dodecahedron with thirty degreeinterior angles, a twenty-four sided icosikaitetragon with fifteendegree interior angles, et cetera. Different three-dimensionalcollapsible structures or tetrahedral building blocks may be formedusing any three or more two-dimensional shapes, including anycombination of arbitrary shapes or regular or irregular close-chainpolygons.

In some embodiments, multiple collapsible structures or tetrahedralbuilding blocks may be connected to form a closed chain polygon (e.g.,triangle, square, pentagon, etc.). The structures may be connected toeach other by magnetic means, by soldering, or by other means.Alternatively, the collapsible structures or tetrahedral building blocksmay be connected to a center hub using one or more spokes percollapsible structure. The connected structures may be configured torotate around the center hub, such as in response to a fluid flow (e.g.,gas or liquid). For example, the connected structures may be used in aturbine configuration, where each collapsible structure is configured tospill and catch air depending on the angles of the planar shapes andorientations of the enhanced devices to cause the connected collapsiblestructures or tetrahedral building blocks to rotate. As another example,the connected structures may be used in a water wheel configuration,where water may contact outer planar shapes and cause the connectedstructures to rotate. The structures may be adjusted to change theangular velocity, rotational direction, or other response of theconnected structures to movement of a fluid across the surface of theenhanced devices. Adjustments may include collapsing or openingindividual planar shapes, or extending or retracting the respectivestructures relative to the hub. In embodiments where the structures areformed from or include a framework comprised of a conductive material,the connected structures may be arranged to form an antenna, such as forterrestrial or satellite communication. The connected structures may beused to conduct vibration, such as in acoustic applications, vibrationtherapy, or other applications. Other hydrodynamic or aerodynamicapplications may be used. In addition to these macroscopic applicationsfor a single or multiple collapsible structures or tetrahedral buildingblocks, collapsible structures or tetrahedral building blocks may beused in various microscopic applications such as nanotechnology. Forexample, multiple microscopic collapsible structures or tetrahedralbuilding blocks may be configured to arrange themselves in a predefinedstructure in the presence of a magnetic field. Similarly, multiplemicroscopic collapsible structures or tetrahedral building blocks may bepermanently arranged in a microscopic structure with predeterminedproperties, such as a resistor, inductor, capacitor, transistor,complete microchip, or other electrical component.

Example 1 includes a six-sided pentagonal structure comprising a firstsubgroup including a first, second, and third substantially pentagonalstructure, the first, second, and third substantially pentagonalstructures arranged to share a first common edge and at least a firstcommon vertex with approximately one hundred and twenty degrees betweenadjacent substantially pentagonal structures, and a second subgroupincluding a fourth, fifth, and sixth substantially pentagonalstructures, the fourth, fifth, and sixth substantially pentagonalstructures arranged to share a second common vertex and a second, third,and fourth common edge with adjacent substantially pentagonal structuresin the second subgroup, wherein the first and second subgroups arearranged such that the first common vertex is collocated with the secondcommon vertex, and the first subgroup first, second, and thirdsubstantially pentagonal structures is arranged to share an edge withthe second subgroup second, third, and fourth common edges,respectively.

Example 2 includes the subject matter of Example 1, further including aplurality of tetrahedral vertex structural supports to support apentagonal vertex connection at each vertex of the first, second, third,fourth, fifth, and sixth substantially pentagonal structures.

Example 3 includes the subject matter of any of Examples 1-2, furtherincluding a plurality of three-sided edge structural supports to supporta plurality of pentagonal edge connections at each edge of the first,second, third, fourth, fifth, and sixth substantially pentagonalstructures.

Example 4 includes the subject matter of any of Examples 1-3, whereinthe plurality of tetrahedral vertex structural supports and theplurality of three-sided edge structural supports are configured toallow at least one of the substantially pentagonal structures tocollapse toward an adjacent substantially pentagonal structure.

Example 5 includes the subject matter of any of Examples 1-4, furtherincluding magnetic material embedded in at least one of thesubstantially pentagonal structures to provide structural support forthe six-sided pentagonal structure.

Example 6 includes the subject matter of any of Examples 1-4, furtherincluding electromagnetic material embedded in at least one of thesubstantially pentagonal structures.

Example 7 includes the subject matter of any of Examples 1-6, whereinthe electromagnetic material is configured, in response to receivingpower, to cause at least one of the sixth substantially pentagonalstructures to collapse toward an adjacent substantially pentagonalstructure.

Example 8 includes the subject matter of any of Examples 1-7, furtherincluding a piezoelectric element embedded in at least one of thesubstantially pentagonal structures configured to generate an electriccharge in response to vibration.

Example 9 includes the subject matter of any of Examples 1-7, whereinthe piezoelectric element is electrically connected to theelectromagnetic material and configured to cause at least one of thesixth substantially pentagonal structures to collapse toward an adjacentsubstantially pentagonal structure in response to the electric chargegenerated by piezoelectric element.

Example 10 includes the subject matter of any of Examples 1-8, furtherincluding a light emitting diode embedded in at least one of thesubstantially pentagonal structures and electrically connected to thepiezoelectric element, wherein the light emitting diode is configured toprovide electroluminescence in response to the electric charge generatedby piezoelectric element.

Example 11 includes the subject matter of any of Examples 1-10, whereinthe light emitting diode is a substantially planar organic lightemitting diode.

Example 12 includes the subject matter of any of Examples 1-11, furtherincluding a first acoustic resonator embedded in at least one of thesubstantially pentagonal structures to induce a vibration in thepiezoelectric element.

Example 13 includes the subject matter of any of Examples 1-12, whereinthe first acoustic resonator is tuned to resonate at a selectedfrequency, and the first acoustic resonator is configured to resonatesympathetically with a second acoustic resonator, and wherein the secondacoustic resonator is external to the six-sided pentagonal structure.

Example 14 includes the subject matter of any of Examples 1-6, whereinthe electromagnetic material is configured, in response to receivingpower, to generate a magnetic field directed in a selected direction.

Example 15 includes the subject matter of Example 1, further includingat least one electrically conductive line embedded in at least one ofthe substantially pentagonal structures, wherein the at least oneelectrically conductive line is configured to convey power or generatean electromagnetic field.

Example 16 includes the subject matter of Example 1, wherein the secondsubgroup is arranged to be connected to a first, second, and thirdexternal subgroups corresponding to a first, second, and third externalsix-sided pentagonal structure to form a substantially regulardodecahedron.

Example 17 includes the subject matter of Example 1, further including aplurality of tetrahedral vertex structural supports to support adodecahedron vertex connection at each vertex of the a substantiallyregular dodecahedron.

Example 18 includes the subject matter of any of Examples 1-14, furtherincluding a plurality of three-sided edge structural supports to supporta plurality of dodecahedron edge connections at each edge of thesubstantially regular dodecahedron.

Example 19 includes a method of making a six-sided pentagonal structurecomprising mounting a first, second, and third substantially pentagonalstructure to share a first common edge and at least a first commonvertex with approximately one hundred and twenty degrees betweenadjacent substantially pentagonal structures to form a first pentagonalsubgroup, mounting a fourth, fifth, and sixth substantially pentagonalstructures to share a second common vertex and a second, third, andfourth common edge with adjacent substantially pentagonal structures inthe second subgroup to form a second pentagonal subgroup, and mountingthe first pentagonal subgroup on the second pentagonal subgroup tocollocate the first common vertex with the second common vertex and toshare an edge on the first, second, and third substantially pentagonalstructures with an edge on the second subgroup second, third, and fourthcommon edges, respectively.

Example 20 includes the subject matter of Example 19, further includingmounting a plurality of tetrahedral vertex structural supports tosupport a pentagonal vertex connection at each vertex of the first,second, third, fourth, fifth, and sixth substantially pentagonalstructures, and mounting a plurality of three-sided edge structuralsupports to support a plurality of pentagonal edge connections at eachedge of the first, second, third, fourth, fifth, and sixth substantiallypentagonal structures.

Example 21 includes a collapsible structure comprising a plurality ofsubstantially planar surfaces hingedly connected, a ferromagneticcomponent fixedly attached to at least one of the plurality ofsubstantially planar surfaces, an electromagnetic component fixedlyattached to at least one of the plurality of substantially planarsurfaces, wherein the applying a current to the electromagneticcomponent causes the electromagnetic component to be attracted to theferromagnetic component, and causes the plurality of substantiallyplanar surfaces to form a selected three-dimensional shape.

This invention is intended to cover all changes and modifications of theexample embodiments described herein that do not constitute departuresfrom the scope of the claims.

What is claimed is:
 1. A building block comprising: a first group offour tetrahedral blocks, each tetrahedral block including four vertices,six edges, and an arcuate hinged flange disposed on each of the sixedges, wherein: a first flange on a first block is attached to a secondflange on a second block; a third flange on the second block is attachedto a fourth flange on a third block; a fifth flange on the third blockis attached to a sixth flange on a fourth block; a seventh flange on thethird block is attached to an eighth flange on the first block; and thefour connected tetrahedral blocks are arranged to form a vertex cluster,the vertex cluster including a first vertex on the first blockcollocated with a second vertex on the second block, with a third vertexon the third block, and with a fourth vertex on the fourth block.
 2. Thebuilding block of claim 1, further comprising: a second group of fourtetrahedral blocks that is identical to the first group of tetrahedralblocks, wherein the first and second groups are coupled to each othervia multiple distal flange groups arranged opposite from respectivevertex clusters.
 3. The building block of claim 1, further comprising: athird group of four tetrahedral blocks that is identical to the firstgroup of tetrahedral blocks, wherein the first and third groups arecoupled to each other via multiple proximal flange groups arrangedadjacent to respective vertex clusters.
 4. The building block of claim1, further comprising electromagnetic material embedded in at least oneof the four tetrahedral blocks to provide a magnetic attachment betweenat least two tetrahedral blocks.
 5. The building block of claim 4,wherein the electromagnetic material is configured, in response toreceiving power, to cause at least one of the flanges to collapse towardan adjacent tetrahedral block.
 6. The building block of claim 5, furthercomprising a piezoelectric element embedded in at least one of the fourtetrahedral blocks configured to generate an electric charge in responseto vibration.
 7. The building block of claim 6, wherein thepiezoelectric element is electrically connected to the electromagneticmaterial and configured to cause at least one of the four tetrahedralblocks to collapse toward an adjacent tetrahedral block in response tothe electric charge generated by piezoelectric element.
 8. The buildingblock of claim 6, further comprising a light emitting diode embedded inat least one of the four tetrahedral blocks and electrically connectedto the piezoelectric element, wherein the light emitting diode isconfigured to provide electroluminescence in response to the electriccharge generated by piezoelectric element.
 9. The building block ofclaim 6, further comprising a first acoustic resonator embedded in atleast one of the four tetrahedral blocks to induce a vibration in thepiezoelectric element, wherein: the first acoustic resonator is tuned toresonate at a selected frequency; and the first acoustic resonator isconfigured to resonate sympathetically with a second acoustic resonator,and wherein the second acoustic resonator is external to the fourtetrahedral blocks.
 10. The building block of claim 1, furthercomprising at least one electrically conductive line embedded in atleast one of the four tetrahedral blocks, wherein the at least oneelectrically conductive line is configured as a communication antenna.11. A kit comprising: a first group of four discs configured to bearranged as a first tetrahedral block; a second group of four discsconfigured to be arranged as a second tetrahedral block; a third groupof four discs configured to be arranged as a third tetrahedral block;and a fourth group of four discs configured to be arranged as a fourthtetrahedral block; wherein: each tetrahedral block includes fourvertices, six edges, and an arcuate hinged flange disposed on each ofthe six edges; and the four tetrahedral block are configured to bemutually connected to form a vertex cluster, the vertex clusterincluding a first vertex on the first block collocated with a secondvertex on the second block, with a third vertex on the third block, andwith a fourth vertex on the fourth block.
 12. The building block ofclaim 11, further comprising: a second group of four tetrahedral blocksthat is identical to the first group of tetrahedral blocks, wherein thefirst and second groups are configured to be coupled to each other viamultiple distal flange groups arranged opposite from respective vertexclusters.
 13. The building block of claim 11, further comprising: athird group of four tetrahedral blocks that is identical to the firstgroup of tetrahedral blocks, wherein the first and third groups areconfigured to be coupled to each other via multiple proximal flangegroups arranged adjacent to respective vertex clusters.
 14. The buildingblock of claim 11, further comprising electromagnetic material embeddedin at least one of the four tetrahedral blocks to provide a magneticattachment between at least two tetrahedral blocks.
 15. The buildingblock of claim 14, wherein the electromagnetic material is configured,in response to receiving power, to cause at least one of the flanges tocollapse toward an adjacent tetrahedral block.
 16. The building block ofclaim 15, further comprising a piezoelectric element embedded in atleast one of the four tetrahedral blocks configured to generate anelectric charge in response to vibration.
 17. The building block ofclaim 16, wherein the piezoelectric element is electrically connected tothe electromagnetic material and configured to cause at least one of thefour tetrahedral blocks to collapse toward an adjacent tetrahedral blockin response to the electric charge generated by piezoelectric element.18. The building block of claim 16, further comprising a light emittingdiode embedded in at least one of the four tetrahedral blocks andelectrically connected to the piezoelectric element, wherein the lightemitting diode is configured to provide electroluminescence in responseto the electric charge generated by piezoelectric element.
 19. Thebuilding block of claim 16, further comprising a first acousticresonator embedded in at least one of the four tetrahedral blocks toinduce a vibration in the piezoelectric element, wherein: the firstacoustic resonator is tuned to resonate at a selected frequency; and thefirst acoustic resonator is configured to resonate sympathetically witha second acoustic resonator, and wherein the second acoustic resonatoris external to the four tetrahedral blocks.
 20. The building block ofclaim 11, further comprising at least one electrically conductive lineembedded in at least one of the four tetrahedral blocks, wherein the atleast one electrically conductive line is configured as a communicationantenna.